Raven P.H., Johnson G.B., Mason K.A. Biology (Ninth Edition)

Подождите немного. Документ загружается.

Apago PDF Enhancer

Figure 12.1

Heredity and family resemblance. Family

resemblances are often strong—a visual manifestation of the

mechanism of heredity.

Figure 12.2

The garden pea,

Pisum sativum. Easy

to cultivate and able to

produce many

distinctive varieties, the

garden pea was a popular

experimental subject in

investigations of

heredity as long as a

century before Gregor

Mendel’s experiments.

Inheritance itself was viewed as traits being borne through

fluid, usually identified as blood, that led to their blending in

offspring. This older idea persists today in the use of the term

“bloodlines” when referring to the breeding of domestic ani-

mals such as horses.

Taken together, however, these two classical assumptions

led to a paradox. If no variation enters a species from outside, and

if the variation within each species blends in every generation,

then all members of a species should soon have the same appear-

ance. It is clear that this does not happen—individuals within

most species differ from one another, and they differ in charac-

teristics that are transmitted from generation to generation.

Early plant biologists produced hybrids

and saw puzzling results

The first investigator to achieve and document successful ex-

perimental hybridizations was Josef Kölreuter, who in 1760

cross-fertilized (or crossed, for short) different strains of tobacco

and obtained fertile offspring. The hybrids differed in appear-

ance from both parent strains. When individuals within the hy-

brid generation were crossed, their offspring were highly

variable. Some of these offspring resembled plants of the hybrid

generation (their parents), but a few resembled the original

strains (their grandparents). The variation observed in second-

generation offspring contradicts the theory of direct transmis-

sion. This can be seen as the beginning of modern genetics.

Over the next hundred years, other investigators elaborated

on Kölreuter’s work. T. A. Knight, an English landholder, in 1823

crossed two varieties of the garden pea, Pisum sativum (figure 12.2).

One of these varieties had green seeds, and the other had yellow

seeds. Both varieties were true-breeding, meaning that the off-

spring produced from self-fertilization remained uniform from

one generation to the next. All of the progeny (offspring) of the

cross between the two varieties had yellow seeds. Among the off-

spring of these hybrids, however, some plants produced yellow

seeds and others, less common, produced green seeds.

Other investigators made observations similar to Knight’s,

namely that alternative forms of observed traits were being dis-

tributed among the offspring. A modern geneticist would say

the alternative forms of each trait were segregating among the

progeny of a mating, meaning that some offspring exhibited one

form of a trait (yellow seeds), and other offspring from the same

mating exhibited a different form (green seeds). This segrega-

tion of alternative forms of a trait provided the clue that led

Gregor Mendel to his understanding of the nature of heredity.

Within these deceptively simple results were the makings

of a scientific revolution. Nevertheless, another century passed

before the process of segregation was fully appreciated.

Mendel used mathematics

to analyze his crosses

Born in 1822 to peasant parents, Gregor Mendel (figure 12.3)

was educated in a monastery and went on to study science and

mathematics at the University of Vienna, where he failed his

examinations for a teaching certificate. He returned to the

monastery and spent the rest of his life there, eventually be-

coming abbot. In the garden of the monastery, Mendel initiated

his own series of experiments on plant hybridization. The re-

sults of these experiments would ultimately change our views of

heredity irrevocably.

Practical considerations for use of the garden pea

For his experiments, Mendel chose the garden pea, the same

plant Knight and others had studied. The choice was a good

one for several reasons. First, many earlier investigators had

produced hybrid peas by crossing different varieties, so Mendel

knew that he could expect to observe segregation of traits

among the offspring.

222

part

III

Genetic and Molecular Biology

rav32223_ch12_221-238.indd 222rav32223_ch12_221-238.indd 222 12/4/09 10:46:27 AM12/4/09 10:46:27 AM

Apago PDF Enhancer

1. The anthers are

cut away on the

purple flower.

Petals

Stigma

Style

Anthers (male)

Carpel (female)

2. Pollen is obtained

from the white

flower.

3. Pollen is

transferred to

the purple flower.

4. All progeny

result in purple

flowers.

Second, a large number of pure varieties of peas were avail-

able. Mendel initially examined 34 varieties. Then, for further

study, he selected lines that differed with respect to seven easily

distinguishable traits, such as round versus wrinkled seeds and yel-

low versus green seeds, the latter a trait that Knight had studied.

Third, pea plants are small and easy to grow, and they

have a relatively short generation time. A researcher can there-

fore conduct experiments involving numerous plants, grow

several generations in a single year, and obtain results rela-

tively quickly.

A fourth advantage of studying peas is that both the male

and female sexual organs are enclosed within each pea flower

(see figure 12.3), and gametes produced by the male and female

parts of the same flower can fuse to form viable offspring, a

process termed self-fertilization. This self-fertilization takes

place automatically within an individual flower if it is not dis-

turbed. It is also possible to prevent self-fertilization by remov-

ing a flower’s male parts before fertilization occurs, then

introduce pollen from a different strain, thus performing cross-

pollination that results in cross-fertilization (see figure 12.3).

Mendel’s experimental design

Mendel was careful to focus on only a few specific differences

between the plants he was using and to ignore the countless

other differences he must have seen. He also had the insight to

realize that the differences he selected must be comparable. For

example, he recognized that trying to study the inheritance of

round seeds versus tall height would be useless.

Mendel usually conducted his experiments in three stages:

1. Mendel allowed plants of a given variety to self-cross for

multiple generations to assure himself that the traits he

Figure 12.3

How Mendel conducted his experiments. In a pea plant  ower,

petals enclose both the male anther (containing pollen grains, which give rise to haploid

sperm) and the female carpel (containing ovules, which give rise to haploid eggs). This

ensures self-fertilization will take place unless the  ower is disturbed. Mendel collected

pollen from the anthers of a white  ower, then placed that pollen onto the stigma of a

purple  ower with anthers removed. This cross fertilization yields all hybrid seeds that

give rise to purple  owers. Using pollen from a white  ower to fertilize a purple  ower

gives the same result.

Inquiry question

What confounding problems could have been seen if Mendel had chosen another

plant with exposed male and female structures?

was studying were indeed true-breeding, that is,

transmitted unchanged from generation to generation.

2. Mendel then performed crosses between true-breeding

varieties exhibiting alternative forms of traits. He also

performed reciprocal crosses: using pollen from a

white- owered plant to fertilize a purple- owered plant,

then using pollen from a purple- owered plant to fertilize

a white- owered plant.

3. Finally, Mendel permitted the hybrid offspring produced by

these crosses to self-fertilize for several generations, allowing

him to observe the inheritance of alternative forms of a trait.

Most important, he counted the numbers of offspring

exhibiting each trait in each succeeding generation.

This quantification of results is what distinguished Mendel’s re-

search from that of earlier investigators, who only noted differences

in a qualitative way. Mendel’s mathematical analysis of experimen-

tal results led to the inheritance model that we still use today.

Learning Outcomes Review 12.1

Prior to Mendel, concepts of inheritance did not form a consistent model.

The dominant view was of blending inheritance, in which traits of parents

were carried by ﬂ uid and “blended” in oﬀ spring. Plant hybridizers before

Mendel, however, had already cast doubt on this model by observing

characteristics in hybrids that seemed to change in second-generation

oﬀ spring. Mendel’s experiments with plants involved quantifying types of

oﬀ spring and mathematically analyzing his observations.

■ Which was more important to Mendel’s success: his

approach, or his choice of experimental material?

chapter

Patterns of Inheritance

223www.ravenbiology.com

rav32223_ch12_221-238.indd 223rav32223_ch12_221-238.indd 223 11/6/09 2:44:57 PM11/6/09 2:44:57 PM

Apago PDF Enhancer

Purple White

Yellow Green

Round Wrinkled

Green Yellow

1. Flower Color

2. Seed Color

3. Seed Texture

4. Pod Color

Dominant Recessive F

Generation

705 Purple:

224 White

3.15:1

6022 Yellow:

2001 Green

3.01:1

5474 Round:

1850 Wrinkled

2.96:1

428 Green:

152 Yellow

2.82:1

Inflated Constricted

5. Pod Shape

882 Inflated:

299 Constricted

2.95:1

Axial Terminal

Tall Short

6. Flower Position

7. Plant Height

651 Axial:

207 Terminal

3.14:1

787 Tall:

277 Short

2.84:1

Figure 12.4

Mendel’s seven traits. Mendel studied how

differences among varieties of peas were inherited when the

varieties were crossed. Similar experiments had been done

before, but Mendel was the  rst to quantify the results and

appreciate their signi cance. Results are shown for seven

different monohybrid crosses. The F

generation is not shown in

the table.

12.2

Monohybrid Crosses: The

Principle of Segregation

Learning Outcomes

Evaluate the outcome of a monohybrid cross.1.

Explain Mendel’s principle of segregation.2.

Compare the segregation of alleles with the behavior of 3.

homologues in meiosis.

A monohybrid cross is a cross that follows only two variations on

a single trait, such as white- and purple-colored flowers. This

deceptively simple kind of cross can lead to important conclu-

sions about the nature of inheritance.

The seven characteristics, or characters, Mendel studied

in his experiments possessed two variants that differed from

one another in ways that were easy to recognize and score

( figure 12.4). We examine in detail Mendel’s crosses with flower

color. His experiments with other characters were similar, and

they produced similar results.

The F

generation exhibits only one

of two traits, without blending

When Mendel crossed white-flowered and purple-flowered

plants, the hybrid offspring he obtained did not have flowers of

intermediate color, as the hypothesis of blending inheritance

would predict. Instead, in every case the flower color of the

offspring resembled that of one of their parents. These off-

spring are customarily referred to as the first filial generation,

or F

. In a cross of white-flowered and purple-flowered plants,

the F

offspring all had purple flowers, as other scientists had

reported before Mendel.

Mendel referred to the form of each trait expressed in the

plants as dominant, and to the alternative form that was not

expressed in the F

plants as recessive. For each of the seven

pairs of contrasting traits that Mendel examined, one of the

pair proved to be dominant and the other recessive.

The F

generation exhibits

both traits in a 3:1 ratio

After allowing individual F

plants to mature and self-fertilize,

Mendel collected and planted the seeds from each plant to see

what the offspring in the second filial generation, or F

would look like. He found that although most F

plants had

purple flowers, some exhibited white flowers, the recessive trait.

Although hidden in the F

generation, the recessive trait had

reappeared among some F

individuals.

Believing the proportions of the F

types would provide

some clue about the mechanism of heredity, Mendel counted

the numbers of each type among the F

progeny. In the cross

between the purple-flowered F

plants, he obtained a total of

929 F

individuals. Of these, 705 (75.9%) had purple flowers,

and 224 (24.1%) had white flowers (see figure 12.4) .

224

part

III

Genetic and Molecular Biology

rav32223_ch12_221-238.indd 224rav32223_ch12_221-238.indd 224 11/6/09 2:44:58 PM11/6/09 2:44:58 PM

Apago PDF Enhancer

generation

(3:1 phenotypic

ratio)

generation

(1:2:1 genotypic

ratio)

Parent generation

True-

breeding

Non-true-

breeding

Non-true-

breeding

True-

breeding

Purple

Dominant

Purple

Dominant

Purple

Dominant

White

Recessive

Self-cross Self-cross Self-cross Self-cross

Cross-fertilize

Self-cross

True-

breeding

Purple

Parent

Purple

Offspring

True-

breeding

White

Parent

Figure 12.5

The F

generation is a disguised 1:2:1 ratio.

By allowing the F

generation to self-fertilize, Mendel found from the

offspring (F

) that the ratio of F

plants was 1 true-breeding dominant:

2 not-true-breeding dominant: and 1 true-breeding recessive.

Approximately ¼ of the F

individuals, therefore, exhibited

the recessive form of the character.

Mendel obtained the same numerical result with the oth-

er six characters he examined: Of the F

individuals, ¾ exhib-

ited the dominant trait, and ¼ displayed the recessive trait (see

figure 12.4). In other words, the dominant-to-recessive ratio

among the F

plants was always close to 3:1.

The 3:1 ratio is actually 1:2:1

Mendel went on to examine how the F

plants passed traits to

subsequent generations. He found that plants exhibiting the re-

cessive trait were always true-breeding. For example, the white-

flowered F

individuals reliably produced white-flowered

offspring when they were allowed to self-fertilize. By contrast,

only ⅓ of the dominant, purple-flowered F

individuals (¼ of

all F

offspring) proved true-breeding , but ⅔ were not. This

last class of plants produced dominant and recessive individuals

in the third filial generation (F

) in a 3:1 ratio.

This result suggested that, for the entire sample, the 3:1

ratio that Mendel observed in the F

generation was really a

disguised 1:2:1 ratio: ¼ true-breeding dominant individuals, ½

not-true-breeding dominant individuals, and ¼ true-breeding

recessive individuals (figure 12.5).

Mendel’s Principle of Segregation

explains monohybrid observations

From his experiments, Mendel was able to understand four

things about the nature of heredity:

■ The plants he crossed did not produce progeny of

intermediate appearance, as a hypothesis of blending

inheritance would have predicted. Instead, different

plants inherited each trait intact, as a discrete

characteristic.

■ For each pair of alternative forms of a trait, one

alternative was not expressed in the F

hybrids, although

it reappeared in some F

individuals. The trait that

“disappeared” must therefore be latent (present but not

expressed) in the F

individuals.

■ The pairs of alternative traits examined were segregated

among the progeny of a particular cross, some individuals

exhibiting one trait and some the other.

■ These alternative traits were expressed in the F

generation in the ratio of ¾ dominant to ¼ recessive.

This characteristic 3:1 segregation is referred to as the

Mendelian ratio for a monohybrid cross.

Mendel’s five-element model

To explain these results, Mendel proposed a simple model that

has become one of the most famous in the history of science,

containing simple assumptions and making clear predictions.

The model has five elements:

Parents do not transmit physiological traits directly to 1.

their offspring. Rather, they transmit discrete information

for the traits, what Mendel called “factors.” We now call

these factors genes .

Each individual receives one copy of each gene from each 2.

parent. We now know that genes are carried on

chromosomes, and each adult individual is diploid, with

one set of chromosomes from each parent.

Not all copies of a gene are identical. The alternative forms 3.

of a gene are called alleles. When two haploid gametes

containing the same allele fuse during fertilization, the

resulting offspring is said to be homozygous. When the

two haploid gametes contain different alleles, the resulting

offspring is said to be heterozygous.

chapter

Patterns of Inheritance

225www.ravenbiology.com

rav32223_ch12_221-238.indd 225rav32223_ch12_221-238.indd 225 11/6/09 2:44:59 PM11/6/09 2:44:59 PM

Apago PDF Enhancer

p pp

p pp pP

p pp

Pp PP

White parent pp

Purple

parent

Purple

heterozygote Pp

Purple

heterozygote

1. p+p=pp. 2. P+p=Pp.

3. p+P=pP. 4. P+P=PP.

generation

generation 3 Purple:1 White

(1PP:2Pp:1pp)

Figure 12.6

Using a Punnett square to analyze Mendel’s cross.

a. To make a Punnett square, place the different female gametes along the side of

a square and the different male gametes along the top. Each potential zygote is

represented as the intersection of a vertical line and a horizontal line. b. In

Mendel’s cross of purple by white  owers, each parent makes only one type of

gamete. The F

are all purple, Pp, heterozygotes. These F

offspring make two

types of gametes that can be combined to produce three kinds of F

offspring: PP

homozygous dominant (purple); Pp heterozygous (also purple); and pp

homozygous recessive (white). The phenotypic ratio is 3 purple:1 white. The

genotypic ratio is 1 PP:2 Pp:1 pp.

and remain distinct—has since been verified in many other or-

ganisms. It is commonly referred to as Mendel’s first law of he-

redity, or the Principle of Segregation. It can be simply stated

as: The two alleles for a gene segregate during gamete formation and

are rejoined at random, one from each parent, during fertilization.

The physical basis for allele segregation is the behavior of

chromosomes during meiosis. As you saw in chapter 11,

homologues for each chromosome disjoin during anaphase I of

meiosis. The second meiotic division then produces ga metes

that contain only one homologue for each chromosome.

It is a tribute to Mendel’s intellect that his analysis arrived

at the correct scheme, even though he had no knowledge of the

cellular mechanisms of inheritance; neither chromosomes nor

meiosis had yet been described.

The Punnett square allows symbolic analysis

To test his model, Mendel first expressed it in terms of a simple

set of symbols. He then used the symbols to interpret his results.

Consider again Mendel’s cross of purple-flowered with

white-flowered plants. By convention, we assign the symbol P

(uppercase) to the dominant allele, associated with the produc-

tion of purple flowers, and the symbol p (lowercase) to the reces-

sive allele, associated with the production of white flowers.

In this system, the genotype of an individual that is true-

breeding for the recessive white-flowered trait would be desig nat-

ed pp. Similarly, the genotype of a true-breeding purple-flowered

The two alleles remain discrete—they neither blend with 4.

nor alter each other. Therefore, when the individual

matures and produces its own gametes, the alleles

segregate randomly into these gametes.

The presence of a particular allele does not ensure that the 5.

trait it encodes will be expressed. In heterozygous individuals,

only one allele is expressed (the dominant one), and the other

allele is present but unexpressed (the recessive one).

Geneticists now refer to the total set of alleles that an individual

contains as the individual’s genotype. The physical appearance

or other observable characteristics of that individual, which re-

sult from an allele’s expression, is termed the individual’s phe-

notype. In other words, the genotype is the blueprint, and the

phenotype is the visible outcome in an individual.

This also allows us to present Mendel’s ratios in more mod-

ern terms. The 3:1 ratio of dominant to recessive is the mono-

hybrid phenotypic ratio. The 1:2:1 ratio of homozygous dominant

to heterozygous to homozygous recessive is the monohybrid ge-

notypic ratio. The genotypic ratio “collapses” into the phenotypic

ratio due to the action of the dominant allele making the heterozy-

gote appear the same as homozygous dominant.

The principle of segregation

Mendel’s model accounts for the ratios he observed in a neat and

satisfying way. His main conclusion—that alternative alleles for

a character segregate from each other during gamete formation

226

part

III

Genetic and Molecular Biology

rav32223_ch12_221-238.indd 226rav32223_ch12_221-238.indd 226 11/6/09 2:44:59 PM11/6/09 2:44:59 PM

Apago PDF Enhancer

Dominant Pedigree

Key

unaffected male

unaffected female

affected male

affected female

Generation I

Generation II

2 1

2 3 4 5 1

2 3 1

Generation III

TABLE 12.1

Some Dominant and Recessive Traits in Humans

Recessive Traits Phenotypes Dominant Traits Phenotypes

Albinism Lack of melanin pigmentation Middigital hair Presence of hair on middle segment of  ngers

Alkaptonuria Inability to metabolize homogentisic acid Brachydactyly Short  ngers

Red-green color blindness Inability to distinguish red or green wavelengths of light Huntington disease Degeneration of nervous system, starting in middle age

Cystic  brosis Abnormal gland secretion, leading to liver degeneration

and lung failure

Phenylthiocarbamide (PTC)

sensitivity

Ability to taste PTC as bitter

Duchenne muscular dystrophy Wasting away of muscles during childhood Camptodactyly Inability to straighten the little  nger

Hemophilia Inability of blood to clot properly, some clots form but

the process is delayed

Hypercholesterolemia

(the most common human

Mendelian disorder)

Elevated levels of blood cholesterol and risk of heart attack

Sickle cell anemia Defective hemoglobin that causes red blood cells to

curve and stick together

Polydactyly Extra  ngers and toes

individual would be designated PP. In contrast, a heterozygote

would be designated Pp (dominant allele first). Using these con-

ventions and denoting a cross between two strains with ×, we can

symbolize Mendel’s original purple × white cross as PP × pp.

Because a white-flowered parent (pp) can produce only p

gametes, and a true-breeding purple-flowered parent (PP, ho-

mozygous dominant) can produce only P gametes, the union of

these gametes can produce only heterozygous Pp offspring in

the F

generation. Because the P allele is dominant, all of these

individuals are expected to have purple flowers.

When F

individuals are allowed to self-fertilize, the P

and p alleles segregate during gamete formation to produce

both P gametes and p gametes. Their subsequent union at fer-

tilization to form F

individuals is random.

The F

possibilities may be visualized in a simple diagram

called a Punnett square, named after its originator, the English

geneticist R. C. Punnett (figure 12.6a ). Mendel’s model, ana-

lyzed in terms of a Punnett square, clearly predicts that the F

generation should consist of ¾ purple-flowered plants and ¼

white-flowered plants, a phenotypic ratio of 3:1 (figure 12.6b).

Some human traits exhibit

dominant/recessive inheritance

A number of human traits have been shown to display both

dominant and recessive inheritance (table 12.1 provides a sam-

ple of these). Researchers cannot perform controlled crosses in

humans the way Mendel did with pea plants, instead geneticists

study crosses that have already been performed—in other

words, family histories. The organized methodology we use is a

pedigree, a consistent graphical representation of matings and

offspring over multiple generations for a particular trait. The

information in the pedigree may allow geneticists to deduce a

model for the mode of inheritance of the trait. In analyzing

these pedigrees, it is important to realize that disease-causing

alleles are usually quite rare in the general population.

A dominant pedigree: Juvenile glaucoma

One of the most extensive pedigrees yet produced traced the

inheritance of a form of blindness caused by a dominant allele.

The disease allele causes a form of hereditary juvenile glauco-

ma. The disease causes degeneration of nerve fibers in the optic

nerve, leading to blindness.

This pedigree followed inheritance over three centuries, fol-

lowing the origin back to a couple in a small town in northwestern

France who died in 1495. A small portion of this pedigree is shown

in figure 12.7 . The dominant nature of the trait is obvious from the

Figure 12.7

Dominant pedigree for hereditary juvenile

glaucoma. Males are shown as squares and females are shown as

circles. Affected individuals are shown shaded. The dominant

nature of this trait can be seen in the trait appearing in every

generation, a feature of dominant traits.

Inquiry question

If one of the affected females in the third generation married

an unaffected male, could she produce unaffected offspring?

If so, what are the chances of having unaffected offspring?

chapter

Patterns of Inheritance

227www.ravenbiology.com

rav32223_ch12_221-238.indd 227rav32223_ch12_221-238.indd 227 11/6/09 2:45:00 PM11/6/09 2:45:00 PM

Apago PDF Enhancer

Recessive Pedigree

Key

unaffected male

unaffected female

affected male

affected female

male carrier

female carrier

Generation I

1 2

1 2 3

5 6 7

Generation II

Generation III

One of these persons

is heterozygous

Heterozygous

Homozygous recessive

Mating between

first cousins

Generation IV

Figure 12.8

Recessive pedigree for albinism. One of the two

individuals in the  rst generation must be heterozygous and individuals

II-2 and II-4 must be heterozygous. Notice that for each affected

individual, neither parent is affected, but both must be heterozygous

(carriers). The double line indicates a consanguineous mating (between

relatives) that, in this case, produced affected offspring.

Inquiry question

From a genetic disease standpoint, why is it never advisable

for close relatives to mate and have children?

12.3

Dihybrid Crosses: The Principle

of Independent Assortment

Learning Outcomes

Evaluate the outcome of a dihybrid cross.1.

Explain Mendel’s Principle of Independent Assortment.2.

Understand the physical basis of independent 3.

assortment.

The Principle of Segregation explains the behavior of alterna-

tive forms of a single trait in a monohybrid cross. The next step

is to extend this to follow the behavior of two different traits in

a single cross: a dihybrid cross.

With an understanding of the behavior of single traits, Men-

del went on to ask if different traits behaved independently in hy-

brids. He first established a series of true-breeding lines of peas

that differed in two of the seven characters he had studied. He then

crossed contrasting pairs of the true-breeding lines to create

heterozygotes. These heterozygotes are now doubly heterozygous,

or dihybrid. Finally, he self-crossed the dihybrid F

plants to pro-

duce an F

generation, and counted all progeny types.

Traits in a dihybrid cross behave independently

Consider a cross involving different seed shape alleles (round,

R, and wrinkled, r) and different seed color alleles (yellow, Y,

and green, y). Crossing round yellow (RR YY) with wrinkled

green (rr yy), produces heterozygous F

individuals having the

same phenotype (namely round and yellow) and the same ge-

notype (Rr Yy). Allowing these dihybrid F

individuals to self-

fertilize produces an F

generation.

The F

generation exhibits four types

of progeny in a 9:3:3:1 ratio

In analyzing these results, we first consider the number of pos-

sible phenotypes. We expect to see the two parental pheno-

types: round yellow and wrinkled green. If the traits behave

independently, then we can also expect one trait from each par-

ent to produce plants with round green seeds and others with

wrinkled yellow seeds.

Learning Outcomes Review 12.2

Mendel’s monohybrid crosses refute the idea of blending. One trait disappears in

the ﬁ rst generation (F

), then reappears in a predictable ratio in the next (F

). The

trait observable in the F

is called dominant, and the other recessive. In the F

the ratio of observed dominant oﬀ spring to recessive is 3:1, and this represents a

ratio of 1 homozygous dominant to 2 heterozygous to 1 homozygous recessive.

The Principle of Segregation states that alleles segregate into diﬀ erent gametes,

which randomly combine at fertilization. The physical basis for segregation is

the separation of homologues during anaphase I of meiosis.

■ What fraction of tall F

plants are true-breeding?

fact that every generation shows the trait. This is extremely un-

likely for a recessive trait as it would require large numbers of un-

related individuals to be carrying the disease allele.

A recessive pedigree: Albinism

An example of inheritance of a recessive human trait is albi-

nism, a condition in which the pigment melanin is not pro-

duced. Long thought to be due to a single gene, multiple genes

are now known that lead to albinism; the common feature is the

loss of pigment from hair, skin, and eyes. The loss of pigment

makes albinistic individuals sensitive to the sun. The tanning

effect we are all familiar with from exposure to the sun is due to

increased numbers of pigment-producing cells, and increased

production of pigment. This is lacking in albinistic individuals

due to the lack of any pigment to begin with.

The pedigree in figure 12.8 is for a form of albinism due

to a nonfunctional allele of the enzyme tyrosinase, which is re-

quired for the formation of melanin pigment. The genetic

characteristics of this form of albinism are: females and males

are affected equally, most affected individuals have unaffected

parents, a single affected parent usually does not have affected

offspring, and affected offspring are more frequent when par-

ents are related. Each of these features can be see in figure 12.8,

and all of this fits a recessive mode of inheritance.

228

part

III

Genetic and Molecular Biology

rav32223_ch12_221-238.indd 228rav32223_ch12_221-238.indd 228 11/6/09 2:45:00 PM11/6/09 2:45:00 PM

Apago PDF Enhancer

RY Ry rY ry

RR YY RR Yy Rr YY Rr Yy

RR Yy RR yy Rr Yy Rr yy

Rr YY Rr Yy rr YY rr Yy

Rr Yy Rr yy rr Yy rr yy

9/16

3/16

1/16

round, yellow

round, green

wrinkled, yellow

wrinkled, green

generation

Cross-Fertilization

Meiosis

(chromosomes assort independently

into four types of gametes)

RY Ry rY ry

X F

(RrYy X RrYy)

Meiosis Meiosis

RR YY rr yy

generation

Parent generation

Rr Yy

Figure 12.9

Analyzing a dihybrid cross. This Punnett

square shows the results of Mendel’s dihybrid cross between plants

with round yellow seeds and plants with wrinkled green seeds. The

ratio of the four possible combinations of phenotypes is predicted to

be 9:3:3:1, the ratio that Mendel found.

Next consider what types of gametes the F

individuals

can produce. Again, we expect the two types of gametes found

in the parents: RY and ry. If the traits behave independently,

then we can also expect the gametes Ry and rY. Using modern

language, two genes each with two alleles can be combined four

ways to produce these gametes: RY, ry, Ry, and rY.

A dihybrid Punnett square

We can then construct a Punnett square with these gametes to

generate all possible progeny. This is a 4 × 4 square with 16

possible outcomes. Filling in the Punnett square produces all

possible offspring (figure 12.9). From this we can see that there

are 9 round yellow, 3 wrinkled yellow, 3 round green, and 1

wrinkled green. This predicts a phenotypic ratio of 9:3:3:1 for

traits that behave independently.

Mendel’s Principle of Independent

Assortment explains dihybrid results

What did Mendel actually observe? From a total of 556 seeds from

self-fertilized dihybrid plants, he observed the following results:

■ 315 round yellow (signified R__ Y__, where the

underscore indicates the presence of either allele),

■ 108 round green (R__ yy),

■ 101 wrinkled yellow (rr Y__ ), and

■ 32 wrinkled green (rr yy).

These results are very close to a 9:3:3:1 ratio. (The expected

9:3:3:1 ratio from this many offspring would be 313:104:104:35.)

The alleles of two genes appeared to behave indepen-

dently of each other. Mendel referred to this phenomenon as

the traits assorting independently. Note that this independent

assortment of different genes in no way alters the segregation of

individual pairs of alleles for each gene. Round versus wrinkled

seeds occur in a ratio of approximately 3:1 (423:133); so do yel-

low versus green seeds (416:140). Mendel obtained similar re-

sults for other pairs of traits.

We call this Mendel’s second law of heredity, or the Prin-

ciple of Independent Assortment. This can also be stated

simply: In a dihybrid cross, the alleles of each gene assort indepen-

dently. A more precise statement would be: the segregation of dif-

ferent allele pairs is independent. This statement more closely ties

independent assortment to the behavior of chromosomes dur-

ing meiosis (see chapter 11). The independent alignment of dif-

ferent homologous chromosome pairs during metaphase I leads

to the independent segregation of the different allele pairs.

Learning Outcomes Review 12.3

Mendel’s analysis of dihybrid crosses revealed that the segregation of allele

pairs for diﬀ erent traits is independent; this ﬁ nding is known as Mendel’s

Principle of Independent Assortment. When individuals that diﬀ er in two

traits are crossed, and their progeny are intercrossed, the result is four

diﬀ erent types that occur in a ratio of 9:3:3:1, Mendel’s dihybrid ratio. This

occurs because of the independent behavior of diﬀ erent homologous pairs

of chromosomes during meiosis I.

■ Which is more important in terms of explaining

Mendel’s laws, meiosis I or meiosis II?

chapter

Patterns of Inheritance

229www.ravenbiology.com

rav32223_ch12_221-238.indd 229rav32223_ch12_221-238.indd 229 11/6/09 2:45:00 PM11/6/09 2:45:00 PM

Apago PDF Enhancer

12.4

Probability: Predicting

the Results of Crosses

Learning Outcomes

Understand the rule of addition and the rule of 1.

multiplication.

Apply the rules of probability to genetic crosses.2.

Probability allows us to predict the likelihood of the outcome

of random events. Because the behavior of different chromo-

somes during meiosis is independent, we can use probability to

predict the outcome of crosses. The probability of an event that

is certain to happen is equal to 1. In contrast, an event that can

never happen has a probability of 0. Therefore, probabilities for

all other events have fractional values, between 0 and 1. For

instance, when you flip a coin, two outcomes are possible; there

is only one way to get the event “heads” so the probability of

heads is one divided by two, or ½. In the case of genetics, con-

sider a pea plant heterozygous for the flower color alleles P and

p. This individual can produce two types of gametes in equal

numbers, again due to the behavior of chromosomes during

meiosis. There is one way to get a P gamete, so the probability

of any particular gamete carrying a P allele is 1 divided by 2 or

½, just like the coin toss.

Two probability rules help predict

monohybrid cross results

We can use probability to make predictions about the outcome

of genetic crosses using only two simple rules. Before we de-

scribe these rules and their uses, we need another definition. We

say that two events are mutually exclusive if both cannot happen

at the same time. The heads and tails of a coin flip are examples

of mutually exclusive events. Notice that this is different from

two consecutive coin flips where you can get two heads or two

tails. In this case, each coin flip represents an independent event.

It is the distinction between independent and mutually exclusive

events that forms the basis for our two rules.

The rule of addition

Consider a six-sided die instead of a coin: for any roll of the die,

only one outcome is possible, and each of the possible outcomes

are mutually exclusive. The probability of any particular num-

ber coming up is  . The probability of either of two different

numbers is the sum of the individual probabilities, or restated

as the rule of addition:

For two mutually exclusive events, the probability of either

event occurring is the sum of the individual probabilities.

Probability of rolling either a 2 or a 6

is =

To apply this to our cross of heterozygous purple F

, four mu-

tually exclusive outcomes are possible: PP, Pp, pP, and pp. The

probability of being heterozygous is the same as the probability

of being either Pp or pP, or ¼ plus ¼, or ½.

Probability of F

heterozygote = ¼Pp + ¼pP = ½

In the previous example, of 379 total offspring, we would ex-

pect about 190 to be heterozygotes. (The actual number is 189.5.)

The rule of multiplication

The second rule, and by far the most useful for genetics, deals

with the outcome of independent events. This is called the

product rule, or rule of multiplication, and it states that

the probability of two independent events both occurring is

the product of their individual probabilities.

We can apply this to a monohybrid cross in which off-

spring are formed by gametes from each of two parents. For

any particular outcome then, this is due to two independent

events: the formation of two different gametes. Consider the

purple F

parents from earlier. They are all Pp (heterozygotes),

so the probability that a particular F

individual will be pp (ho-

mozygous recessive) is the probability of receiving a p gamete

from the male (½) times the probability of receiving a p gamete

from the female (½), or ¼:

Probability of pp homozygote = ½p (male parent) × ½p

(female parent) = ¼pp

This is actually the basis for the Punnett square that we

used before. Each cell in the square was the product of the

probabilities of the gametes that contribute to the cell. We then

use the addition rule to sum the probabilities of the mutually

exclusive events that make up each cell.

We can use the result of a probability calculation to pre-

dict the number of homozygous recessive offspring in a cross

between heterozygotes. For example, out of 379 total offspring,

we would expect about 95 to exhibit the homozygous recessive

phenotype. (The actual calculated number is 94.75.)

Dihybrid cross probabilities are based

on monohybrid cross probabilities

Probability analysis can be extended to the dihybrid case. For

our purple F

by F

cross, there are four possible outcomes,

three of which show the dominant phenotype. Thus the prob-

ability of any offspring showing the dominant phenotype is ¾,

and the probability of any offspring showing the recessive phe-

notype is ¼. Now we can use this and the product rule to pre-

dict the outcome of a dihybrid cross. We will use our example

of seed shape and color from earlier, but now examine it using

probability.

If the alleles affecting seed shape and seed color segregate

independently, then the probability that a particular pair of al-

leles for seed shape would occur together with a particular pair of

alleles for seed color is the product of the individual probabilities

for each pair. For example, the probability that an individual with

wrinkled green seeds (rr yy) would appear in the F

generation

would be equal to the probability of obtaining wrinkled seeds

(¼) times the probability of obtaining green seeds (¼), or 

Probability of rr yy = ¼ rr × ¼ yy = 

rr yy

230

part

III

Genetic and Molecular Biology

rav32223_ch12_221-238.indd 230rav32223_ch12_221-238.indd 230 11/6/09 2:45:01 PM11/6/09 2:45:01 PM

Apago PDF Enhancer

Dominant

Phenotype

(unknown

genotype)

PP or Pp?

Homozygous

recessive

Homozygous

dominant

If Pp If PP

then then

Alternative 1:

All offspring are purple

and the unknown flower

is homozygous dominant

Homozygous

recessive

Heterozygous

dominant

Alternative 2:

Half of the offspring are

white and the unknown flower

is heterozygous dominant

Figure 12.10

A testcross. To determine whether an individual exhibiting a dominant phenotype, such as purple  owers, is homozygous

or heterozygous for the dominant allele, Mendel crossed the individual in question with a plant that he knew to be homozygous recessive—in

this case, a plant with white  owers.

Because of independent assortment, we can think of the

dihybrid cross of consisting of two independent monohybrid

crosses; since these are independent events, the product rule

applies. So, we can calculate the probabilities for each dihy-

brid phenotype:

Probability of round yellow (R__ Y__) =

¾ R__ × ¾ Y__ =

Probability of round green (R__ yy) =

¾ R__ × ¼ yy =

Probability of wrinkled yellow (rr Y__) =

¼ rr × ¾ Y__ =

Probability of wrinkled green (rr yy) =

¼ rr ×¼ yy =

The hypothesis that color and shape genes are indepen-

dently sorted thus predicts that the F

generation will display a

9:3:3:1 phenotypic ratio. These ratios can be applied to an ob-

served total offspring to predict the expected number in each

phenotypic group. The underlying logic and the results are the

same as obtained using the Punnett square.

Learning Outcomes Review 12.4

The rule of addition states that the probability of either of two events

occurring is the sum of their individual probabilities. The rule of

multiplication states that the probability of two independent events

both occurring is the product of their individual probabilities. These

rules can be applied to genetic crosses to determine the probability of

particular genotypes and phenotypes. Results can then be compared

against these predictions.

■ How would you calculate the probability of all

dominant phenotype F

progeny in a trihybrid cross?

12.5

The Testcross: Revealing

Unknown Genotypes

Learning Outcome

Interpret data from test crosses to infer genotypes.1.

To test his model further, Mendel devised a simple and power-

ful procedure called the testcross. In a testcross, an individual

with unknown genotype is crossed with the homozygous reces-

sive genotype—that is, the recessive parental variety. The con-

tribution of the homozygous recessive parent can be ignored,

because this parent can contribute only recessive alleles.

Consider a purple-flowered pea plant. It is impossible to

tell whether such a plant is homozygous or heterozygous simply

by looking at it. To learn its genotype, you can perform a test-

cross to a white-flowered plant. In this cross, the two possible test

plant genotypes will give different results (figure 12.10) :

Alternative 1: Unknown individual is homozygous dominant

(PP ) PP × pp: All offspring have purple  owers (Pp).

Alternative 2: Unknown individual is heterozygous (Pp)

Pp × pp: ½ of offspring have white  owers (pp), and

½ have purple  owers (Pp).

Put simply, the appearance of the recessive phenotype in

the offspring of a testcross indicates that the test individual’s

genotype is heterozygous.

For each pair of alleles Mendel investigated, he ob-

served phenotypic F

ratios of 3:1 (see figure 12.4) and test-

cross ratios of 1:1, just as his model had predicted.

Testcrosses can also be used to determine the genotype of

an individual when two genes are involved. Mendel often

chapter

Patterns of Inheritance

231www.ravenbiology.com

rav32223_ch12_221-238.indd 231rav32223_ch12_221-238.indd 231 11/6/09 2:45:01 PM11/6/09 2:45:01 PM